Einstein’s Other Blunder
Hello, I'm Kay Strang. You can check me out at my website, quantumid.science, where you can find more detailed analysis and material on my series of six podcasts, hunting the identity of the quantum. The first podcast looked at the ultraviolet catastrophe and illustrated how the problem really was the result of using out-of-date mathematics. As far as I know, there have been no attempts to solve the problem using vector calculus, but this is hardly surprising as both Oliver Heavyside and W. J. Gibbs, who came up with vector calculus, are pretty much ignored in most textbooks on the history of physics.
There is, however, another perhaps more compelling argument supporting the particle view of light or radiation involving the photoelectric effect. Nevertheless, it still involves faulty reasoning, mistaking mathematical expediency for an ontological truth. So let's look at what I consider to be Einstein's other blunder. It is well documented that Einstein considered his cosmological constant to be a blunder, but was later recognised as a necessary part of cosmology, whereas he was awarded the Nobel Prize for his 1905 paper on, amongst other things his interpretation of the photoelectric effect, which supported the idea of a quanta or package of energy rather than a continuous wave.
The photoelectric effect had been discovered by Hertz in 1887. In experiments that fired a beam of light at a sheet of metal, for example, potassium, the light dislodged electrons from the metal. The odd factor was that the increase in the intensity or energy of the light beam did not on its own result in more electrons being freed. It was the frequency of the light beam that was critical. So light of a specific frequency would free electrons of the same frequency. What was later described, I think, by Schrödinger, as a bookkeeping exercise by nature arose and delivered an account balance in the transaction of light and matter. This view of nature required light to be formed of discrete packets of energy, quantified using Planck’s constant multiplied by the frequency, and later rechristened ‘photons’.
In reaching this conclusion, Einstein had used the analogy of Joules’ ideal gas law, which was based on point-like particles. This is very similar to Rayleigh and Jeans using statistical mechanics designed for averaging out the energy of a finite quantity of gas molecules to continuous radiation, resulting in the so-called ultraviolet catastrophe. It doesn't work. Einstein's account, of course, flew in the face of Maxwell's equations and undermined wave phenomena such as interference, reflection, diffraction, and refraction, and so on. Most major physicists of the day, such as J. J. Thompson and Arnold Sommerfeld, rejected Einstein's quantum account of the photoelectric effect and derived it from purely classical principles. This fact seems to get lost in many historical accounts. Also Schrödinger considered it could be explained in terms of resonance phenomena between two identical wave frequencies.
In 1923, A. H. Compton conducted scattering experiments to prove Einstein's theory. An analysis of these experiments is included in the additional material section to this podcast on the website quantumid.science. Briefly, the experiments were criticised as inconclusive. Notwithstanding this, the door had been opened for the development of the Copenhagen interpretation of quantum mechanics supported by Heisenberg, Max Born, and others. It prevailed against the wave theory of light supported by Schrödinger and despite some reservations by Niels Bohr.
Bohr in his Nobel lecture in 1922 stated,
‘ . . . in spite of its heuristic value, the hypothesis of light quanta, which is quite irreconcilable with so called interference phenomena, is not able to throw light on the nature of radiation.’
Again, Bohr in discussions with Einstein struggled to accept the characterization of light as streams of photons. He states.
‘ . . . notwithstanding its fertility, the idea of the photon implied a quite unforeseen dilemma, since any simple corpuscular picture of radiation would obviously be irreconcilable with interference effects, which present so essential an aspect of radiative phenomena, and can be described only in terms of a wave picture. The acuteness of the dilemma is stressed by the fact that the interference effects offer our only means of defining the concepts of frequency and wavelength entering into the very expression for the energy and momentum of the photon.’
I take this to mean that Bohr knew that in defining the energy of a photon as h times f, that is Planck's constant times frequency, that Einstein and Planck were effectively digitizing wave phenomena. He concludes that Louis De Broglie in 1925 extending wave particle duality to material particles had exacerbated the problem.
‘The paradoxical aspects of quantum theory were in no way ameliorated but even emphasized by the apparent contradiction between the exigencies of the general superposition principle of the wave description and the feature of individuality of the elementary atomic processes.’
Bohr tried to effect a compromise, resulting unfortunately in the notion of wave particle duality, which only confuses matters.
Although phenomena can be treated mathematically as waves or particles, I believe particles are imposters, not only in relation to radiation, but also to matter. The atomic theory or corpuscular theory of matter was discredited centuries ago in discussions between Newton and Leibniz, and the question is why it prevails today in the form of the standard model. Like Planck, Einstein had committed an ontological error in trying to shoehorn continuous phenomena into discrete particle-like entities. The key problem was not that an instrumentalist approach was adopted over a scientific realist approach, but that the former was dressed up as scientific realism. I believe Einstein, who later criticised the Copenhagen interpretation of quantum mechanics, may have regretted his youthful error. So if one takes this view, it is obvious Einstein’s analysis of the photoelectric effect was a blunder of greater proportion than the cosmological constant.
Check out www.quantumid.science where you will find more in-depth downloadable essays, book lists, additional material, and original papers by some 19th and 20th century physicists. The third podcast is titled Heisenberg, The Salieri of Physics, which examines how Heisenberg sabotaged his rival Schrödinger.
© K. Strang 2025
